A307088 The position function the fractalization of which yields A307081.

1, 2, 2, 4, 2, 6, 2, 8, 5, 7, 2, 12, 2, 9, 9, 15, 2, 17, 2, 19, 10, 13, 2, 24, 9, 15, 13, 23, 2, 28, 2, 29, 13, 19, 13, 35, 2, 21, 15, 37, 2, 37, 2, 32, 29, 24, 2, 48, 14, 34, 19, 37, 2, 48, 18, 50, 21, 30, 2, 60, 2, 31, 38, 56, 20, 51, 2, 47, 25, 52, 2, 71

Offset

1,2

Comments

For a definition of the fractalization process, see comments in A194959. The sequence A307081, triangular array where row n is the list of the numbers from 1 to n sorted in ascending order of f(n) = A095112(n)/n, is clearly the result of a fractalization. Let {a(n)} (this sequence) be its position function.

Links

Table of n, a(n) for n=1..72.

Formula

a(n)=1 iff n=1.

a(n)=2 iff n is a prime number.

a(n)=n iff n is in A307187.

Example

In A307081 in triangular form,
- row 8 is:  1  7  5  3  2  4  6  8
- row 9 is:  1  7  5  3  9  2  4  6  8
Row 9 is row 8 in which 9 has been inserted in position 5, so a(9) = 5.

Prog

(PARI) f(n)={my(s=0, T); T=factorint(n); for(i=1, #T[, 1], for(j=1, T[i, 2], s+=1/T[i, 1]^j)); s}
prog(n)={my(V, v, j); V=List(); for(k=1, n, v=f(k)+0.; j=setsearch(V, v, 1); if(j==0, print("err"); return, listinsert(V, v, j); print1(j, ", ")))}

Crossrefs

Cf. A194959 (introducing fractalization).

Cf. A307081 (fractalization of this sequence).

Cf. A307187 (positions of the records of f).

Cf. A095112.

Sequence in context: A316437 A137502 A318885 * A143112 A286472 A279690

Adjacent sequences: A307085 A307086 A307087 * A307089 A307090 A307091

Keyword

nonn

Author

Luc Rousseau, Mar 23 2019

Status

approved